Low-cost minimum-time line-broadcasting schemes in complete binary trees

Broadcasting is the process of transmitting a message from a member in a network (originator) to all other members. A line-broadcasting scheme allows two members to communicate during one time unit as long as there is a path of lines between them and no link is used in more than one call between two members. Farley [3] showed an algorithm that accomplishes line broadcasting in any tree on n vertices in minimum time, which is [log₂ n] time units. Since the structure of the tree is unknown in advance, the total number of communication link uses (cost) of his scheme is Θ(n - 1)[log₂ n]. In this paper, we present line-broadcasting schemes for complete binary trees. The cost of the algorithms is linear in the number of vertices. This answers a question raised by Fujita and Farley [5].